This invention relates generally to encoding and decoding of binary data transmitted over partial response channels using maximum likelihood sequence detection (PRML). More particularly, this invention relates to a method for developing a non-quasicatastrophic and phase invariant matched spectral null trellis code having a preselected code rate, wherein the order of the higher order null in the transfer function of the partial response channel is .gtoreq.1.
Methods for encoding binary data for recordation on storage media such as a computer disk, and for subsequent decoding of retrieved data are generally known in the art. In this regard, data coding and decoding methods have been developed with a view toward maximizing data storage density and media storage capacity while permitting rapid data storage and subsequent retrieval at a minimum error rate. Such methods have included matched spectral null codes of the so-called trellis type, designed for use in a partial response system having a transfer function of the form (1-D)(1+D).sup.n, identified typically as the dicode, PR4, EPR4 and E.sup.2 PR4 channels for n=0, 1, 2 and 3, respectively. Matched spectral null codes of this type are known in theory to provide signal-to-noise (SNR) gain in the course of data storage and retrieval.
Matched spectral null trellis codes including background theory related thereto are described in more detail in Karabed and Siegel, Matched Spectral-Null Codes For Partial-Response Channels, IEEE Transactions On Information Theory, Vol. 37, No. 3, p. 818 (May 1991), which is incorporated by reference herein. See also U.S. Pat. Nos. 4,888,775; 4,888,779 and 5,095,484.
Despite the discussion of such trellis codes in the printed literature, and the theoretical benefits which would arise from their use, matched spectral null codes which are both phase invariant and non-quasicatastrophic and also match the higher order null of a partial response system with n.gtoreq.2, have not been developed. In this regard, it is known that the data recording density increases in direct proportion to the value of (n), and hence it is desirable to utilize the higher order channels where n=2 and n=3. Mowever, to date, these trellis codes have been limited to partial response systems, for n=0, and for n=1, such that it has not been possible in actual practice to take maximum advantage of the higher order channels.
The present invention is specifically directed to overcoming this problem, by providing a matched spectral null trellis code which can be used on higher order partial response systems, i.e., n=2 and n=3.